The paper presents an elegant approach for designing linear phase low pass digital FIR filter using swarm and evolutionary algorithms. Classical gradient based approaches are not efficient enough for accurate design and thus evolutionary approach is considered to be a better choice. In this paper a hybrid of Genetic Algorithm and Particle Swarm Optimization algorithm with varying neighbourhood topology, namely Genetic Lbest Particle Swarm Optimization with Dynamically Varying Neighbourhood (GLPSO DVN) is used to find the filter coefficients. In this work two objective functions (error metrics) are minimized. The first one is based on stop and pass band ripple and the second one studies the mean square error between the ideal and actual designed filter. The hybrid algorithm is found to produce fitter candidate solution than the classical Lbest PSO. The results are compared with the results obtained by solving the same problem using Lbest PSO (LPSO). It is also observed that GLPSO DVN gives better results than LPSO and as well LPSO DVN.